estimation of ionospheric tec and faraday rotation …05.pdf · estimation of ionospheric tec and...

Estimation of Ionospheric TEC and Faraday Rotationfor L-Band SAR

Michael Jehle, Maurice Ruegg, David Small, Erich Meier and Daniel Nuesch

Remote Sensing Laboratories, University of Zurich, CH-8057 Zurich, Switzerland

ABSTRACT

Spaceborne synthetic aperture radar (SAR) systems are used to measure geo- and biophysical parameters of the earth’s sur-face, e.g. for agriculture, forestry and land subsidence investigations. Upcoming SAR sensors such as the Japanese PhasedArray L-band Synthetic Aperture Radar (PALSAR) onboard the Advanced Land Observing Satellite (ALOS) exemplify atrend towards lower frequencies and higher range chirp bandwidth in order to obtain additional information with highergeometric resolution. However, the use of large bandwidths causes signal degradation within a dispersive medium such asthe ionosphere. Under high solar activity conditions at L-band frequencies, ionosphere-induced path delays and Faradayrotation become significant for SAR applications. Due to ionospheric effects, blind use of a generic matched filter causesinaccuracy when correlating the transmitted with the received signal. Maximum correlation occurs where the length of thematched filter, based on a synthetic chirp model of the transmitted signal, is adjusted to correspond to that of the receivedsignal. By searching for the proper adjustment necessary to reach this maximum, the change in length can be estimatedand used to derive variations in the total electron content (TEC) and degree of Faraday rotation within the ionosphere fromall range lines in a SAR image.

Keywords: Synthetic Aperture Radar, Ionosphere, Total Electron Content, Faraday Rotation

1. INTRODUCTION

Knowledge of attitude and position of spaceborne SAR sensors has improved in recent years.1 Concerning geometricaccuracy, the importance of atmospheric path delay increases with continuing improvements to the resolution of SARsystems surveying the Earth and other planets. Contributions of atmosphere-induced path delays must be estimated in orderto be able to attain a geolocation accuracy independent of atmospheric influences. Atmospheric path delay contributions atL-band frequencies are mainly due to ionospheric influences. In addition to geometry, estimates of Faraday rotation (FR)are necessary to properly calibrate polarimetric data and derived products.An overview of ionospheric effects and FR is provided in Section 2 and Section 3. Section 4 exemplifies the method -amodel of wave radiation for chirp pulses and pulse compression for a SAR system is presented. Section 5 deals with thesimulation and theory of an expected chirp shortening under conditions of low and relatively high solar activity conditions.Section 6 shows simulated examples for states of average and high solar activity for both existing and upcoming spaceborneSAR missions. In the last section, limitations, assumptions and conclusions implicit to the method are discussed.

2. IONOSPHERIC DELAY

The earth’s ionosphere located between the altitudes of approximately 50 - 1500 km, is characterized by the existence offree electrons and ions that influence the refractive index in this area. The degree of ionization is caused mainly by solarUV radiation and depends on the local atmospheric density. The TEC specifies the number of free electrons in a columnwith a cross section of 1 m2 along the signal path and is defined as2

TEC =∫

h

Nedh. (1)

Ne [ em3 ] is the electron density along the ray path h. TEC units (TECU) are defined to be 1016 electrons per m2. TEC

is usually low at night and maximum at round 14:00 local time, when the sun’s position is approximately two hours pastzenith. The extent of this time shift depends on the time light needs to ionize the layer to the maximum.Maximum electron density is found in the so called F2-layer of the ionosphere at a height of approximately 350 km. Thedegree of ionization, i.e. the number of free electrons interacting with the traversing signal, causes a path delay that depends

Remote Sensing of Clouds and the Atmosphere X, edited by Klaus Schäfer, Adolfo Comerón,James R. Slusser, Richard H. Picard, Michel R. Carleer, Nicolaos Sifakis,

Proc. of SPIE Vol. 5979, 59790U, (2005) · 0277-786X/05/$15 · doi: 10.1117/12.627618

Proc. of SPIE Vol. 5979 59790U-1

a'

mainly on the signal’s carrier frequency f . This dispersive behavior can be used to estimate the TEC along the ray path.GPS stations, for example, measure the time delay at two frequencies L1 and L2, calculate global TEC over a network ofabout 200 receiving stations, providing GPS users with ionosphere correction terms through the navigation message. Dailymaps of global TEC are published on the Internet (e.g. www.aiub.unibe.ch/ionosphere/).Based on Ref. 3, we can describe the path delay ∆s through the ionosphere for electromagnetic waves traveling from asatellite to the earth and back by:

∆s = 2 K · TEC

f2 · cos α(2)

α [degrees] denotes the satellite off-nadir angle, and K= 40.28 [ m3

s2 ] is the refractive constant.3 The factor 1cos α accounts

approximately for the slant range direction. The quadratic dependency on frequency term indicates that increasinglysignificant path delays occur at lower frequencies. Table 1 shows expected path delays at L-band for average and highsolar conditions. For an incidence angle of 39 degrees, path delays at C-band are between 2 m and 5.5 m and between 0.5m to 1.5 m for X-band. Figure 1 shows mean levels at 13:00 h UTC of global vertical TEC for 1998 and 2002. The mapswere calculated using the global ionospheric maps (GIM) from the International GPS Service (IGS). TEC level estimatesare sampled every 5 degrees in longitude and 2.5 degrees in latitude.2

Longitude in degrees

Latit

ude

in d

egre

es

Low solar activity: mean TEC levels of year 1998, 13:00 h UTC

−180 −90 0 90 180

90

45

0

−45

−90


Latit

ude

in d

egre

es

High solar acitvity: mean TEC levels of year 2002, 13:00 h UTC

−180 −90 0 90 180

90

45

0

−45

−90 0

20

40

60

80

100

[TEC

U]

Figure 1. Mean TEC levels calculated by averaging 365 GIMs obtained from the IGS. Left: 1998, 13:00 h with average solar conditions.Right: 2002, 13:00 h where TEC levels were around solar maximum.

3. FARADAY ROTATION

In addition to the ionosphere-induced path delay described above, which manifests itself as a range shift in spaceborneSAR images, the ionosphere also induces a small polarization-dependent effect which can become significant at L-bandor lower frequencies. The free electrons of the ionosphere interact with the traversing electromagnetic wave resultingin a rotation Ω of the polarization vector. When a linearly polarized wave enters an ionized medium in the presence ofan external magnetic field, one can treat the radar wave as split into two oppositely rotating circularly polarized wavestraveling at slightly different velocities and along slightly different ray paths. When the two components recombine at thesatellite or reach the ground, the resultant linear polarization is different from the initial value.4 Given the knowledge oflocal TEC levels and a model of the earth’s magnetic field B (e.g. CO2-model5), the degree of Faraday rotation FR can beestimated using6, 7:

Ω =2.365 · 104

c2· λ2

h∫

0

Ne · B cos θ sec α dh (3)

= 2.610−13 · TEC · B · λ2 cos θ , α = 0

where λ [m] is the wavelength of the electromagnetic wave and θ [degrees] is the angle between the magnetic field and the


- e—-----ThLongitude in degrees

Latit

ude

in d

egre

es

Levels of Faraday rotation for mean TEC in 2002 (at L−band), 13:00 h UTC

−180 −90 0 90 180

90

45

0

−45

−90

−10

−5

0

5

10

[deg

]


Latit

ude

in d

egre

es

Levels of Faraday rotation for mean TEC in 1998 (at L−band), 13:00 h UTC

−180 −90 0 90 180

90

45

0

−45

−90

Figure 2. Typical levels of one-way Faraday rotation at low and high solar conditions. Based on the calculated mean TEC levels for1998 and 2002 in Section 2 (see Figure 1) Faraday rotation and the magnetic field is estimated each with day of year (DOY) 202 andvertical incidence angle.

radar wave. α is set to zero for vertical incidence relative to the earth center. Equation (3) refers to one-way propagationthrough the ionosphere. For SAR applications the effect doubles.6

Current TEC estimation methods use a Global Navigation Satellite System (GNSS) network to derive TEC maps togetherwith a magnetic field model to predict FR. Figure 2 shows estimated FR at L-band for average and high solar conditionsin 1998 and 2002. For every pixel the incidence angle relative to the earth center is vertical. To estimate the influenceof the ionosphere under low and high solar conditions the mean TEC maps from Figure 1 were used. The magnetic fieldcomponent was calculated for a height of 100 to 450 km from the CHAMP/Ørsted/Ørsted-2 model (CO2-model5) for July21, 1998 and July 21, 2002, respectively. It is clearly visible that under high solar conditions FR can limit polarimetricanalysis in mid-latitude regions.Another widely used method can be applied when the sensor has a fully polarimetric mode by making use of the factthat backscatter measurement reciprocity (HV=VH) is violated in the presence of FR. By comparing the cross-polarizedterms of the scattering matrix,8 an estimate of the degree of FR may be made. This method has the advantage of notrequiring data from outside the sensor environment - however the satellite must acquire the data in full polarimetric mode(full scattering matrix).

4. FREQUENCY MODULATION

Spaceborne imaging radar systems transmit modulated pulses to improve resolution in range at a manageable peak power.The most commonly used method is a linear frequency modulation of the transmitted pulse st, (called a chirp), which is asine wave with constantly increasing (up-chirp) or decreasing (down-chirp) frequency during its pulse duration. Figure 3(a)and (b) show a down-chirp in time and frequency plots. The chirp pulse was simulated using JERS-1 parameters fromTable 1.The following two subfigures show the chirp pulse after baseband conversion in time (Figure 3(c)) and frequencydomains (Figure 3(d)) respectively. After conversion to baseband the chirp shows symmetry at about half of the pulselength in time and about 0 Hz in the frequency domain (Figure 3(d)). For illustrative reasons (c) shows only a segmentfrom the whole pulse. A discrimination between up- and down-chirps from Figure 3(c) and (d) is no longer possible. Witha start frequency fstart of

fstart = fc + B/2 (4)

and a stop frequency fstop offstop = fc − B/2 (5)


0 1 2 3 4

x 10−5

−1

−0.5

0

0.5

1

(a) simulation of L−band chirp

time [s]

real

par

t of s

ent c

hirp

0 0.5 1 1.5 2 2.5 3 3.5

x 10−5

1.266

1.268

1.27

1.272

1.274

1.276

1.278

1.28

1.282

1.284x 10

9 (b) frequency−response curve

time [s]

freq

uenc

y [H

z]

1 1.5 2 2.5

x 10−5

−1

−0.5

0

0.5

1(c) chirp after baseband conversion

time [s]

real

par

t of s

ent c

hirp

−8 −6 −4 −2 0 2 4 6 8

x 106

0

5

10

15

20

25

30

35(d) frequency−response curve in baseband

frequency [Hz]

pow

er s

pect

ral d

ensi

ty P

SD

Figure 3. (a) Simulated JERS-1 chirp pulse in time domain. (b) plot illustrating the chirp’s frequency-dependency on time. (c) chirppulse in baseband. Pulse form is symmetric about half of the pulse duration. For illustrative purposes, only half of the pulse duration isshown. (d) Power spectrum of baseband converted chirp pulse.

which are located half the bandwidth B off the chirp’s carrier frequency fc, a chirp can be written as:

st(t, Tt) = Ut · ej2π(fstartt+ktt2) · rect[0, Tt] (6)

kt = − B

2Tt

Ut amplitude of the transmitted signalkt chirp rate [1/s2]Tt chirp duration of the transmitted pulse [s]rect[0, Tt] square pulse of amplitude 1 and length Tt [unitless]

From (6) the phase of the chirp waveform is given as

φ(t) = 2π(fstartt + ktt

2). (7)

The instantaneous frequency of the chirp can then be calculated by

f(t) =12π

dφ(t)dt

= fstart + 2ktt. (8)

The received signal sr(t) at the antenna can be written as:

sr(t, Tr) = Ur · ej2π(frt+krt2) · rect[0, Tr]. (9)


with

Ur amplitude of the received signalfr starting frequency of the received chirp [Hz]kr chirp rate of received signal [1/s2]Tr chirp duration for the received signal [s]rect[0, Tr] rectangular pulse of amplitude 1 and length Tr [unitless]

To focus a radar image along a range line the received frequency modulated pulses at the antenna are first down-convertedto baseband. They are then compressed through matched filtering. This corresponds to convolution of the measured signalwith the complex conjugate of the transmitted chirp s∗t . Mathematically, a convolution is the cross correlation function(CCF) of time reversed i.e. complex conjugate signals. For range compression for the matched filter one has:

CCF (Tt, Tr) = s∗t (t, Tt) ∗ sr(t, Tr)

=1

maxTt, Tr ·∫ maxTt,Tr/2

−maxTt,Tr/2

s∗t (t, Tt) · sr(t + τ, Tr)dt

= F−1St(w)∗ · Sr(w) (10)

As shown above a computationally efficient method to solve this equation is to calculate the product of the signals in thefrequency domain and estimate the CCF in time-domain over the inverse Fourier transform.

5. SIMULATION OF CHIRP SHORTENING

The principle of a matched filter as described in Section 4 is sketched in Figure 4. The frequency modulated transmittedsignal is compared with the received chirp signal of a point target. Simulating an up-chirp, the received signal is shortened

0time

edutilpma

time

ampl

itude

time

ampl

itude

CCFt∆

2

t∆

00

0.2

0.8

1

time

edutilpm

a

0

0.2

0.8

1

Figure 4. Simulated correlation of two chirps. The chirps, differing in pulse duration correlate suboptimally and appear defocused andshifted. An iterative procedure correlates within an interval defined by the range of expected TEC until a maximum correlation is found.


because higher frequency chirp segments return slightly faster to the satellite antenna than lower frequency parts that aredelayed slightly longer in the ionosphere. Comparing transmitted vs. received pulses the shortening influences neither thebandwidth nor the start and stop frequency of the transmitted pulse but does change the chirp rate k.Concerning range resolution, the reflected signal passes through a filter that delays it to an extent that is a function offrequency. As mentioned above the filter function corresponds to the cross correlation of the transmitted signal with thereceived signal. To obtain maximum correlation, it is necessary to know both the chirp rate and duration of the receivedsignal. In conventional SAR applications the filter function is implemented using the autocorrelation, implicitly assumingthat the form of the received chirp signal corresponds exactly to that of the transmitted chirp. Signals influenced by theionosphere correlate suboptimally and may appear defocused and shifted in range. A way to solve this problem is to modifythe synthesized reference transmit signal before correlating so that a maximum correlation is achieved. One can changethe length of the pulse duration of the transmitted chirp in steps of ∆t to find

CFF (∆tTEC) = maxCCF (Tt + n · ∆t, Tr) with n ε [nmin, nmax] (11)

where nmin and nmax delimit the search space, and

∆t(nmax − nmin) (12)

covers the entire theoretically possible shortening time range. ∆tTEC represents the time delay from the synthesisedtransmitted chirp at which a maximum in correlation is reached.Referring to Section 2, path delays caused by the ionosphere depend on the TEC and on the carrier frequency accordingto (2). The higher the bandwidth and the lower the carrier frequency of the chirp the more significant the change in lengthof the received chirp becomes. The ionosphere’s dispersive behavior shortens a transmitted up-chirp; down-chirps arebroadened. An estimated change in length ∆tTEC within the pulse duration of a chirp may be used to estimate the TECvalue along the ray path:

TEC =12· ∆tTEC · c

K·(

f2start · f2

stop

f2start − f2

stop

)(13)

In order to illustrate the behavior of the maximum in correlation over different chirp lengths, Figure 5 illustrates a dis-tribution with two simulated chirps. The properties for the chirps were again chosen for the JERS-1 case (down-chirp atL-band). One chirp is set to constant length and duration and simulates the received chirp. The other changes its lengthand chirp rate from shorter to longer. Figure 5(a) shows an example given that the signal passed the ionosphere without

0.999

0.9995

1

(a) Simulation of L−band chirp correlation -no ionospheric delay

0 25 50 75 100 125TEC [TECU]

amou

nt o

f cor

rela

tion

0.999

0.9995

1

(b) Simulation of L−band chirp correlation with ionospheric delay

amou

nt o

f cor

rela

tion

-1.5 -1.2 -0.9 -0.6 -0.3 0 0.3 0.6 0.9 1.2 1.5Change in chirp length [m]

0 25 50 75 100 125TEC [TECU]

-1.5 -1.2 -0.9 -0.6 -0.3 0 0.3 0.6 0.9 1.2 1.5Change in chirp length [m]

Figure 5. Simulation of maxima in correlation for two chirps, where one is set to a constant chirp length and the other is shortened. (a)assumes that the ionosphere has no influence on the chirp length. (b) assuming that the received chirp was broadened.

any change to its length. As expected, correlation is highest when the lengths of the two chirps are equal at 0 TEC, whereno difference in length and chirp rate is expected. In a situation where the received chirp is broadened, e.g. due to a TECof 50, the absolute maximum in the graph of Figure 5(b) shifts to higher TEC values on the right.


6. SIMULATION FOR SPACEBORNE L-BAND SAR SENSORS

As mentioned previously, radar systems at L-band or lower frequency are strongly affected by the ionosphere. Data foranalysis is rare or currently not adequate for accurate examination. In the following, a 3D-simulation for a point target withreference sensor configurations was made to give an impression of how spaceborne SAR sensors can be affected underrelatively high and normal ionospheric conditions. Interesting sensor configurations are JERS-1, ALOS PALSAR andTerraSAR-L -all operating at L-band, with a broad range of bandwidths. Table 1 shows details for the respective sensors.A detailed description of the system model is available in Ref. 9.

Sensor Units TerraSAR-L ALOS PALSAR JERS-1Frequency (fc) [GHz] 1.2575 1.27 1.275Range bandwidth B [MHz] 85 28 15Chirp duration [µsec] 35 28 35Sampling rate [MHz] 102∗ 33.6∗ 17.1Chirp form Upchirp Downchirp DownchirpOrbit (altitude) [km] 629 695 580Simulated TEC [TECU] 0 60 150 0 60 150 0 60 150Off-nadir α [deg.] 39 39 39 39 39 39 39 39 39Path delay at fc (2-way) [m] 0 39.3 98.3 0 38.6 96.4 0 36.4 91.0Change in received [m] 0 -5.33 -13.32 0 1.7 4.25 0 0.86 2.14chirp length3 dB width [m] 2.13 4.71 12.48 6.45 6.47 6.54 12.05 12.05 12.06Difference in [dB] 0 -1.13 -5.68 0 0.013 -0.076 0 -0.001 -0.007amplitude ∆t=0 vs. ∆tmax

Peak sidelobe ratio (PSLR) [dB] -6.63 -6.20 -1.76 -6.63 -6.57 -6.24 -6.63 -6.63 -6.61∗Sampling rates for TerraSAR-L and ALOS PALSAR were assumed using typical oversampling factors.

Table 1. Satellite sensor details and estimates of influence of 0, 60, 150 TECU on the path delay, the 3 dB bandwidth, amplitude andPSLR, based on simulations.

6.1. TerraSAR-L

With a possible launch after 2006, a low center frequency, and a high bandwidth for a SAR-system, the returned signals

−1 −0.5 0 0.5 1x 10

−7

−15

−10

−5

0received signal at 60 TECU (grey), 0 TECU (black)

time [sec]

ampl

itude

[dB]

−1 −0.5 0 0.5 1

x 10−7

−15

−10

−5


time [sec]

ampl

itude

[dB]

2.67 m6.65 m

Figure 6. Simulated response function of cross correlation for TerraSAR-L at 60 and 150 TECU.


of TerraSAR-L as simulated in Figure 6 would be expected to degrade extremely under high solar conditions. Simulationassuming 150 TECU shows that the uncompensated 3 dB bandwidth spreads to over 12 m.

6.2. ALOS PALSARFigure 7 shows results of simulations based on ALOS PALSAR parameters. PALSAR, a SAR system at L-band frequencywith smaller bandwidth and a launch planned in late 2005 should have less degradation in resolution. At L-band frequen-cies, the system should be capable of detecting ionospheric changes with a sensitivity that depends on the sensors samplingfrequency.

−1 −0.5 0 0.5 1x 10

−7

−15

−10

−5


time [sec]

]Bd[ edutilpma

−1 −0.5 0 0.5 1

x 10−7

−15

−10

−5


time [sec]

]Bd[ edutilpma

0.85 m 2.13 m

Figure 7. Simulated response function of the cross correlation for ALOS PALSAR at 60 and 150 TECU.

6.3. JERS-1 (1992 - 1998)Figure 8 shows because of a relatively low bandwidth compared to ALOS and TerraSAR-L, TEC estimation with JERS-1is made more difficult. A limiting factor for the detection of TEC at 5 TECU sensitivity is the 17 MHz sampling rate. The

−1 −0.5 0 0.5 1x 10

−7

−15

−10

−5

0

time [sec]

]Bd[ edutilpma

−1 −0.5 0 0.5 1

x 10−7

−15

−10

−5


time [sec]

]Bd[ edutilpma

0.42 m 1.07 m

received signal at 60 TECU (grey), 0 TECU (black)

Figure 8. Simulated response function of the cross correlation for JERS-1 at 60 and 150 TECU.

small 15 MHz bandwidth causes relatively small changes in chirp length, close to practicable detection limits.


7. CONCLUSION

High resolution spaceborne SAR sensors such as the upcoming PALSAR on ALOS provide possibilities for detecting slantpath delays of electromagnetic wave propagation through the ionosphere. Caused by the frequency dependent runtime ofa radar signal through the ionosphere, the change in length of a chirp signal could be measured by searching for the properadjustment necessary to reach a maximum in correlation of the transmitted and received signal. Simulations of ALOS,TerraSAR-L and JERS-1 show that an estimation of TEC levels within each range line of a SAR scene with a sensitivity ofapproximately 5 TECU might be possible. First results with JERS-1 data show good agreement with values derived fromglobal GPS-TEC maps and motivate further investigations. Extracting TEC levels from spaceborne SAR sensors or otherradar instruments such as altimeters which use chirp-like waveforms could provide support for future estimates of Faradayrotation, antenna range biases or slant mapping of TEC values. SAR-derived TEC levels can be used for an autonomouscalibration of ionospheric effects on SAR images. Limitations are set by the respective sensor sampling frequencies, thechirp bandwidth and the overlying noise.

REFERENCES

1. D. Small, B. Rosich, A. Schubert, E. Meier, and D. Nuesch, “Geometric Validation of Low and High-Resolution ASARImagery,” Proceedings of the 2004 Envisat and ERS Symposium ESA SP-572, p. 9, Apr. 2005.

2. S. Schaer, “Mapping and Predicting the Earth’s Ionosphere Using the Global Positioning System,” Geodatisch-geophysikalische Arbeiten in der Schweiz 59, 1999.

3. R. F. Hanssen, Radar Interferometry., vol. 2, Kluwer Academic Publishers, 2001.4. R. Fitzpatrick, “Faraday Rotation.” http://farside.ph.utexas.edu/teaching/em/lectures/

node101.html, 2005.5. R. Holme, “CO2-A CHAMP magnetic field model.” http://www.dsri.dk/Oersted/Field_models/

CO2/.6. P. A. Wright, S. Quegan, N. S. Wheadon, and C. D. Hall, “Faraday Rotation Effects on L-Band Spaceborne Data.,”

IEEE Transactions on Geoscience and Remote Sensing 41, pp. 2735–2744, Dec. 2003.7. E. J. M. Rignot, “Effect of Faraday Rotation on L-Band Interferometric and Polarimetric Synthetic-Aperture Radar

Data.,” IEEE Transactions on Geoscience and Remote Sensing 38, pp. 383–390, Dec. 2000.8. A. Freeman, “Calibration of Linearly Polarized Polarimatric SAR Data Subject to Faraday Rotation,” IEEE Transac-

tions on Geoscience and Remote Sensing 42, pp. 1617–1624, Aug. 2004.9. M. Soumekh, Synthetic Aperture Radar Signal Processing., vol. 1, John Wiley & Sons, Inc., 1999.


estimation of ionospheric tec and faraday rotation …05.pdf · estimation of ionospheric tec and...

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